Alex Salmond is on the brink of a significant political victory at the European elections, with many Labour voters in Scotland threatening to stay at home in protest at the Westminster expenses scandal.

Senior Labour figures fear large numbers of supporters will refuse to vote this Thursday, greatly increasing the prospects of the Scottish National party taking the largest share of the votes.

That would be a significant propaganda coup for Salmond, allowing him to claim that the SNP is now established as Scotland's largest political party, and a further heavy blow to Gordon Brown.

Salmond is keen to bolster his government's influence in Brussels, and believes Thursday's result will help the SNP bypass the UK government within the European commission.

The SNP is focused on mobilising its core vote, arguing that its MEPs would be the strongest advocates for Scotland in Europe and urging its supporters to use Thursday to punish Brown's government over the expenses scandal.

Salmond launched the final phase of their campaign – which has been entirely overshadowed by the expenses crisis – in the SNP's latest stronghold, Dundee, on Tuesday.

"The Westminster government is crumbling, its authority has drained away, and SNP success on Thursday will force the UK government to act on key Scottish demands as well as forcing the pace on an early general election, and delivering a strong Scottish voice in Europe," he said.

Salmond now claims the European election is a "straight two-horse race" with Labour. He is very likely to win on the popular vote. But Salmond's hopes that the SNP might snatch three of the six seats available in Scotland appear to have been dashed by the jump in support for smaller parties due to the expenses crisis.

Opinion polls before the crisis suggested that the SNP could have taken 34% of the vote and the Liberal Democrats only 11%. Under Europe's proportional voting system, that result would have handed the SNP three seats and left the Lib Dems with none.

Yet support for the Lib Dems, and the Greens, appears to have strengthened in the last month, increasing the Lib Dems' confidence they will win a seat. But neither the UK Independence party nor the BNP have made any great gains in Scotland, unlike in other parts of the UK.

Labour sources admit their greatest fear is winning only one seat on Thursday, humiliating Gordon Brown on his home ground. Recent UK opinion polls put Labour at 17% – the worst figure in party history. However, a YouGov poll for the Daily Telegraph suggests Labour support is stronger in Scotland, at 24%, only five points behind the SNP.

"We know it will be a difficult fight to maintain Labour as the largest party, but we're obviously trying very hard," said one official.

Professor John Curtice, an elections expert at the University of Strathclyde, says this suggests that both Labour and the SNP will win two seats each on Thursday – the key issue is who wins the largest popular vote.

"The election in Scotland has always been about who can come first in votes," he said. "If the Labour party is able to come first in votes they will be able to say the shine has come off Alex Salmond.

"If the SNP comes first in votes, they will be able to say they're still the most popular party. The battle for credibility is crucial here."

The precise size of the SNP vote could hinge on votes from the Outer Hebrides, which are likely to be the last votes counted in Britain. The Western Isles follow strict Sabbatarian rules and refuse to count votes on a Sunday, so its ballot papers from their 22,000 voters will not be totted up until Monday morning, when the final result will be declared in Edinburgh.